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On the Clustered Steiner Tree Problem

  • Conference paper
Combinatorial Optimization and Applications (COCOA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8287))

Abstract

We investigate the Clustered Steiner tree problem on metric graphs, which is a variant of Steiner minimum tree problem. The required vertices are partitioned into clusters, and in a feasible clustered Steiner tree, the subtrees spanning two different clusters must be disjoint. In this paper, we show that the problem remains NP-hard even if the topologies of all clusters and the inter-cluster tree are given. We propose a (ρ + 2)-approximation algorithm for the general case, in which ρ is the approximation ratio for the Steiner tree problem. When the topologies for all clusters are given, we show a (ρ + 1)-approximation algorithm. We also discuss the Steiner ratio for this problem. We show the ratio is lower and upper bounded by three and four, respectively.

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Author information

Authors and Affiliations

  1. National Chung Cheng University, ChiaYi, 621, Taiwan, R.O.C.

    Bang Ye Wu

Authors
  1. Bang Ye Wu
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Editor information

Editors and Affiliations

  1. Institute of Theoretical Computer Science, ETH Zürich, Zürich, Switzerland

    Peter Widmayer

  2. State Key Lab for Manufacturing Systems Engineering, 710049, Xi’an, China

    Yinfeng Xu

  3. Department of Computer Science, Montana State University, 59717-3880, Bozeman, MT, USA

    Binhai Zhu

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© 2013 Springer International Publishing Switzerland

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Wu, B.Y. (2013). On the Clustered Steiner Tree Problem. In: Widmayer, P., Xu, Y., Zhu, B. (eds) Combinatorial Optimization and Applications. COCOA 2013. Lecture Notes in Computer Science, vol 8287. Springer, Cham. https://doi.org/10.1007/978-3-319-03780-6_6

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  • DOI: https://doi.org/10.1007/978-3-319-03780-6_6

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03779-0

  • Online ISBN: 978-3-319-03780-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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